Introduction:
In Lewis's model of economic development, the labor supply in the traditional agricultural sector is often assumed to be perfectly inelastic. However, over time, this perfectly inelastic labor supply gradually becomes inelastic due to various factors. This gradual transformation can be explained by analyzing the dynamics of the Lewis model.

Explanation:

1. Perfectly Inelastic Labor Supply:
- In the initial stages of development, the labor supply in the traditional agricultural sector is perfectly inelastic. This means that the number of workers in the sector remains constant regardless of changes in wages or other economic factors.
- The labor supply is perfectly inelastic because most of the labor force is engaged in subsistence agriculture and is unable to find alternative employment opportunities. They are trapped in the agricultural sector due to limited education, skills, and lack of capital.

2. Rural-urban migration:
- As the industrial sector grows, urban areas attract labor from the rural agricultural sector. This phenomenon is known as rural-urban migration.
- The industrial sector offers higher wages and better employment opportunities, which incentivizes workers to move from the traditional agricultural sector to the industrial sector.
- The migration of labor from the agricultural sector to the industrial sector reduces the labor supply in agriculture, making it relatively more inelastic.

3. Limited absorption capacity:
- As the industrial sector expands, it reaches a point where it can no longer absorb all the surplus labor from the agricultural sector.
- The industrial sector has limited absorption capacity due to factors such as capital constraints, technological limitations, and market demand.
- This limited absorption capacity leads to a gradual decrease in the rate of rural-urban migration, resulting in a less elastic labor supply in the agricultural sector.

4. Structural changes:
- With industrialization, there are structural changes in the economy, such as the growth of the service sector and the emergence of new industries.
- These structural changes create additional employment opportunities outside of agriculture.
- As the economy diversifies, the labor supply in the agricultural sector becomes relatively less elastic as workers have more options for employment in different sectors.

5. Government policies:
- Government policies can also influence the elasticity of labor supply in the agricultural sector.
- Policies promoting education, skill development, and rural infrastructure can enhance the mobility of labor and reduce the dependency on agriculture.
- By providing alternative employment opportunities and improving rural livelihoods, government policies can contribute to the gradual transformation of labor supply from perfectly inelastic to inelastic.

Conclusion:
In Lewis's model, the perfectly inelastic labor supply in the traditional agricultural sector gradually becomes inelastic due to rural-urban migration, limited absorption capacity of the industrial sector, structural changes in the economy, and government policies. These factors collectively contribute to the transformation of the labor supply, enabling the economy to move towards industrialization and economic development.